Abstract

An automated technique for adaptive radar polarimetric pattern classification is described. The approach is based on a genetic algorithm that uses a probabilistic pattern separation distance function and searches for those transmit and receive states of polarization sensing angles that optimize this function. Seven pattern separation distance functions—the Rayleigh quotient, the Bhattacharyya, divergence, Kolmogorov, Matusta, Kullback–Leibler distances, and the Bayesian probability of error—are used on real, fully polarimetric synthetic aperture radar target signatures. Each of these signatures is represented as functions of transmit and receive polarization ellipticity angles and the angle of polarization ellipse. The results indicate that, based on the majority of the distance functions used, there is a unique set of state of polarization angles whose use will lead to improved classification performance.

© 2006 Optical Society of America

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References

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  1. L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).
  2. F. A. Sadjadi and A. Mahalanobis, "Target-adaptive polarimetric synthetic aperture radar target discrimination using maximum average correlation height filters," Appl. Opt. 45, 3063-3070 (2006).
    [CrossRef] [PubMed]
  3. F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 37, 38-49 (2002).
    [CrossRef]
  4. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).
  5. J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. 35, 818-825 (1987).
    [CrossRef]
  6. F.T.Ulaby and C.Elachi, eds., Radar Polarimetry for Geoscience Applications (Artech House, 1990).
  7. H. Mott, Antennas for Radar and Communications: a Polarimetric Approach (Wiley, 1992).
  8. S. Huard, Polarization of Light (Wiley, 1996).
  9. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).
  10. M. I. Skolnik, Introduction to Radar Systems, 2nd ed. (McGraw-Hill, 1980).
  11. R. O. Duda, and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, 1973).
  12. P. A. Devijver and J. Kittler, Pattern Recognition: a Statistical Approach (Prentice-Hall International, 1982).
  13. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).
  14. Z. Michalewicz, Genetic Algorithm + Data Structures = Evolutionary Programs, 2nd ed. (Springer 1992).
  15. J. Holland, Adaptation in Natural and Artificial Systems (MIT Press, 1992).

2006 (1)

2002 (1)

F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 37, 38-49 (2002).
[CrossRef]

1990 (1)

L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).

1987 (1)

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. 35, 818-825 (1987).
[CrossRef]

Butrl, M. C.

L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).

Chaney, R. D.

L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).

Devijver, P. A.

P. A. Devijver and J. Kittler, Pattern Recognition: a Statistical Approach (Prentice-Hall International, 1982).

Duda, R. O.

R. O. Duda, and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, 1973).

Elachi, C.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. 35, 818-825 (1987).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Hart, P. E.

R. O. Duda, and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, 1973).

Holland, J.

J. Holland, Adaptation in Natural and Artificial Systems (MIT Press, 1992).

Huard, S.

S. Huard, Polarization of Light (Wiley, 1996).

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

Kittler, J.

P. A. Devijver and J. Kittler, Pattern Recognition: a Statistical Approach (Prentice-Hall International, 1982).

Mahalanobis, A.

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithm + Data Structures = Evolutionary Programs, 2nd ed. (Springer 1992).

Mott, H.

H. Mott, Antennas for Radar and Communications: a Polarimetric Approach (Wiley, 1992).

Novak, L. M.

L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).

Owirka, G. J.

L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).

Papas, C. H.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. 35, 818-825 (1987).
[CrossRef]

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).

Sadjadi, F. A.

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems, 2nd ed. (McGraw-Hill, 1980).

van Zyl, J. J.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. 35, 818-825 (1987).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Aerosp. Electron. Syst. (1)

F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 37, 38-49 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. 35, 818-825 (1987).
[CrossRef]

Lincoln Lab. J. (1)

L. M. Novak, M. C. Butrl, R. D. Chaney, and G. J., Owirka, "Optimal processing of polarimetric synthetic aperture radar imagery," Lincoln Lab. J. 3, 273-290 (1990).

Other (11)

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).

F.T.Ulaby and C.Elachi, eds., Radar Polarimetry for Geoscience Applications (Artech House, 1990).

H. Mott, Antennas for Radar and Communications: a Polarimetric Approach (Wiley, 1992).

S. Huard, Polarization of Light (Wiley, 1996).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

M. I. Skolnik, Introduction to Radar Systems, 2nd ed. (McGraw-Hill, 1980).

R. O. Duda, and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, 1973).

P. A. Devijver and J. Kittler, Pattern Recognition: a Statistical Approach (Prentice-Hall International, 1982).

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Z. Michalewicz, Genetic Algorithm + Data Structures = Evolutionary Programs, 2nd ed. (Springer 1992).

J. Holland, Adaptation in Natural and Artificial Systems (MIT Press, 1992).

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Figures (9)

Fig. 1
Fig. 1

Sample of public domain polarimetric SAR image used in the experiment.

Fig. 2
Fig. 2

Variations of target separations using the Rayleigh quotient.

Fig. 3
Fig. 3

GA optimum set for the Rayleigh quotient metric.

Fig. 4
Fig. 4

Variations of target separations using the Bhattacharyya distance.

Fig. 5
Fig. 5

GA optimum set for the Bhattacharyya metric.

Fig. 6
Fig. 6

Variations of target separations using the divergence distance.

Fig. 7
Fig. 7

GA optimum set for divergence metric.

Fig. 8
Fig. 8

Variations of target separations using the Kullback–Leibler distance.

Fig. 9
Fig. 9

GA optimum set for the Kullback–Leibler metric.

Tables (2)

Tables Icon

Table 1 Relation of Polarimetric Signatures aij and bkl to Angle Values χ and ψ

Tables Icon

Table 2 Optimum Transmit–Receive Ellipticity Angle and Angle of Polarization

Equations (31)

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S = [ | S H H | e ϕ H H | S H V | e ϕ H V | S H V | e ϕ H V | S V V | e ϕ V V ] ,
P r = k | E r E t | 2 ,
P r = k A r [ K ] A t .
A = [ E H E H * + E V E V * E H E H * E V E V * 2 Re [ E H E V * ] 2 Im [ E H E V * ] ] = [ a 2 a 2 cos 2 χ cos 2 ψ a 2 cos 2 χ sin 2 ψ a 2 sin 2 χ ] ,
E = Re { [ E H h + E V v ] e j ( κ r ω t ) } ,
K 11 = ( | S H H | 2 + 2 | S H V | 2 + | S V V | 2 ) ,
K 12 = K 21 = ( | S H H | 2 | S V V | 2 ) ,
K 13 = K 31 = Re ( S H H S H V * + S H V S V V * )
K 14 = K 41 = Im ( S H H S H V * + S H V S V V * ) ,
K 22 = ( | S H H | 2 2 | S H V | 2 + | S V V | 2 ) ,
K 23 = K 32 = Re ( S H H S H V * S H V S V V * ) ,
K 24 = K 42 = Im ( S H H S H V * S H V S V V * ) ,
K 33 = Re ( S H H S V V * + | S H V | 2 ) ,
K 34 = K 43 = Im ( S H H S V V * ) ,
K 44 = Re ( S H H S V V * + | S H V | 2 ) ,
σ r t ( ψ r , χ r , ψ t , χ t ) = lim r ( 4 π r 2 P r p t ) ,
σ ( ψ r , χ r , ψ t , χ t ) = 4 π A r [ K ] A t .
p ( ω 1 ) = p ( ω 2 ) = 0.5.
J ( w ) = w T S B w w T S w w ,
S B = ( m 1 m 2 ) ( m 1 m 2 ) T ,
S w = i = 1 , 2 x ω i w T ( x m i ) ( x m i ) T w .
w = S w - 1 ( m 1 m 2 ) ,
p Bhattacharyya = ( p 1 ) 1 / 2 ( p 2 ) 1 / 2 exp [ μ ( 1 2 ) ] ,
μ ( 1 / 2 ) = ln L [ p ( x | ω 1 ) 1 / 2 ( p ( x | ω 2 ) ] 1 / 2 d x .
E D = 1 8 exp ( J D 2 ) ,
E D E = Bayesian   probability   of   error ,
J D = [ p ( x | ω 1 ) p ( x | ω 2 ) ] ln p ( x | ω 1 ) p ( x | ω 2 ) d x .
J T = { [ p ( x | ω 1 ) p ( x | ω 2 ) d x } 1 / 2 .
J KL = p ( x | ω 1 ) ln p ( x | ω 1 ) p ( x | ω 2 ) d x .
J K = | p ( x | ω 1 ) p 1 p ( x | ω 2 ) p 2 | d x .
E = min [ p ( ω 1 | x ) , p ( ω 2 | x ) ] p ( x ) d x .

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